Unfortunately "back up" does not mean "back up everything".
(You think it would... but it doesn't. Not sure why Apple thinks you want to lose 1000s of emails... but you will. Instantly and without any warning.)
Your only choices are based on 2 things that its already too late for you to change:
If you "kept email on server"... you can have it resent to your phone.
(Unfortunately, you will also get 1000s of email you do NOT want. Ugh.)
If you didn't "keep email on server"... you lost everything.
Kind of odd that "backing up" CAUSES you to have a massive data-loss. But unfortunately, some non-thinking people at Apple do it that way.
Not sure why "back up my email" would have been so impossible for Apple to do. (Or at least give you the choice. I'm pretty sure nearly everyone would say "YES, KEEP MY EMAIL".)
Or, at least the back-up process should say in huge letters: "You are about to lose 100% of your email." Before you start. (No, you have to later read about it buried in the docs somewhere.)
I would imagine if enough people contacted Apple about this "feature" they might do something about it.